Method for efficient volumetric integration for 3D sensors

ABSTRACT

A vehicle, system and method of mapping the environment is disclosed. The system includes a sensor and a processor. The sensor is configured to obtain a detection from an object in an environment surrounding the vehicle. The processor is configured to compute a plurality of radial components and a plurality of angular components for a positive inverse sensor model (ISM) of an occupancy grid, select a radial component corresponding to a range of the detection from the plurality of radial components and selecting an angular component corresponding to an angle of the detection from the plurality of angular components, multiply the selected radial component and the selected angular component to create an occupancy grid for the detection, and map the environment using the occupancy grid.

INTRODUCTION

The subject disclosure relates to methods for mapping an environmentusing one or more radar systems and, in particular, to using a negativeinverse sensor model that is updatable via a quad-tree structure to forman occupancy grid to represent the environment.

Radar systems can be employed on vehicles to sense objects in anenvironment of the vehicle for the purpose of mapping the environment,or objects in the environment. Such maps can be used to navigate thevehicle through the environment without coming into contact with objectsin the environment. One method of processing radar signals includescreating a volumetric occupancy grid that records locations of theobject in the form of probabilities based on detections from the radarsystem. The occupancy grid can be created and updated using a dualinverse sensor model (ISM) that includes a positive ISM and a negativeISM. One important aspect of mapping an environment using an occupancygrid is being able to update the occupancy grid in order to reflect thecurrent state of the environment and objects in the environment.Accordingly, it is desirable to provide a method of mapping theenvironment that updates at least the negative ISM quickly andefficiently.

SUMMARY

In one exemplary embodiment, a method of mapping the environment isdisclosed. The method includes computing a plurality of radialcomponents and a plurality of angular components for a positive inversesensor model (ISM) of an occupancy grid, obtaining a detection at asensor from an object in an environment surrounding the vehicle,selecting a radial component corresponding to a range of the detectionfrom the plurality of radial components and selecting an angularcomponent corresponding to an angle of the detection from the pluralityof angular components, multiplying the selected radial component and theselected angular component to create an occupancy grid for thedetection, and mapping the environment using the occupancy grid.

In addition to one or more of the features described herein, the ISMfurther comprises a negative ISM and a probability value of the negativeISM is assigned using a quad-tree structure of the occupancy grid. Anode of the quad-tree structure corresponds to a solid angle and a firstlevel of the quad-tree structure includes solid angle bins that combineto cover a field of view of the sensor. The method further includespartitioning a solid angle bin at a level of the quad-tree structureinto a plurality of sub solid angles at a sub level of the quad-treestructure when the solid angle bin at the level is includes thedetection. The method further includes assigning a probability value toa solid angle bin for which there is no detection, wherein theprobability value reflects an absence of the detection in the solidangle bin. The method further includes combining the probability valuesfrom the negative ISM with a probability value from the positive ISM tocreate the occupancy grid. In various embodiments, the method includesnavigating the vehicle with respect to the object based on the mappingof the environment.

In another exemplary embodiment, a system for mapping an environment ata vehicle is disclosed. The system includes a sensor and a processor.The sensors is configured to obtain a detection from an object in anenvironment surrounding the vehicle. The processor is configured tocompute a plurality of radial components and a plurality of angularcomponents for a positive inverse sensor model (ISM) of an occupancygrid, select a radial component corresponding to a range of thedetection from the plurality of radial components and selecting anangular component corresponding to an angle of the detection from theplurality of angular components, multiply the selected radial componentand the selected angular component to create an occupancy grid for thedetection, and mapping the environment using the occupancy grid.

In addition to one or more of the features described herein, theprocessor is further configured to assign a probability value of anegative ISM of the occupancy grid using a quad-tree structure of theoccupancy grid. A node of the quad-tree structure corresponds to a solidangle and a first level of the quad-tree structure includes solid anglebins that combine to cover a field of view of the sensor. The processoris further configured to partition a solid angle bin at a level of thequad-tree structure into a plurality of sub solid angles at a sub levelof the quad-tree structure when the solid angle bin at the levelincludes the detection. The processor is further configured to assign aprobability value to a solid angle bin for which there is no detection,wherein the probability value reflects an absence of the detection atthe solid angle bin. The processor is further configured to combine theprobability values from the negative ISM with a probability value from apositive ISM to create the occupancy grid. In various embodiments, theprocessor is configured to navigate the vehicle with respect to theobject based on the mapping of the environment.

In yet another exemplary embodiment, a vehicle is disclosed. The vehicleincludes a sensor and a processor. The sensor is configured to obtain adetection from an object in an environment surrounding the vehicle. Theprocessor is configured to compute a plurality of radial components anda plurality of angular components for a positive inverse sensor model(ISM) of an occupancy grid, select a radial component corresponding to arange of the detection from the plurality of radial components andselecting an angular component corresponding to an angle of thedetection from the plurality of angular components, multiply theselected radial component and the selected angular component to createan occupancy grid for the detection, and mapping the environment usingthe occupancy grid.

In addition to one or more of the features described herein, theprocessor is further configured to assign a probability value to anegative ISM of the occupancy grid using a quad-tree structure of theoccupancy grid. A node of the quad-tree structure corresponds to a solidangle and a first level of the quad-tree structure includes solid anglebins that combine to cover a field of view of the sensor. The processoris further configured to partition a solid angle bin at a level of thequad-tree structure into a plurality of sub solid angles at a sub levelof the quad-tree structure when the solid angle bin at the levelincludes the detection. The processor is further configured to assign aprobability value to a solid angle bin for which there is no detection,wherein the probability value reflects an absence of the detection atthe solid angle bin. The processor is further configured to combine theprobability values from the negative ISM with a probability value from apositive ISM to create the occupancy grid.

The above features and advantages, and other features and advantages ofthe disclosure are readily apparent from the following detaileddescription when taken in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features, advantages and details appear, by way of example only,in the following detailed description, the detailed descriptionreferring to the drawings in which:

FIG. 1 shows a vehicle with an associated trajectory planning systemdepicted at in accordance with various embodiments;

FIG. 2 shows an illustrative occupancy grid;

FIG. 3a (prior art) shows a radial probability graph for creating orupdating an occupancy grid based on an object's location;

FIG. 3b (prior art) shows a log(odds) model for a radial probabilitygraph of an object located at a selected range;

FIG. 4 shows an occupancy grid illustrating regions of no detections;

FIG. 5 shows an illustrative quad-tree structure that can be used tostore and update probability values for a negative ISM;

FIG. 6 illustrates us of the quad-tree structure of FIG. 5 to fill anoccupancy grid using a negative ISM;

FIG. 7 shows positive ISM, a negative ISM, and a dual ISM for anoccupancy grid;

FIG. 8 shows a flow diagram illustrating a method for producing anoccupancy grid that dynamically represents an environment of the vehicleof FIG. 1;

FIG. 9 shows a display of an illustrative radar field in a scenario inwhich an object is passing in front of the vehicle, wherein the radarfield is formed from an occupancy grid that does not use the negativeISM; and

FIG. 10 shows the display of the illustrative radar field in the samescenario as FIG. 9, wherein the radar field is formed from an occupancygrid that uses the negative ISM disclosed herein.

DETAILED DESCRIPTION

The following description is merely exemplary in nature and is notintended to limit the present disclosure, its application or uses. Itshould be understood that throughout the drawings, correspondingreference numerals indicate like or corresponding parts and features.

In accordance with an exemplary embodiment, FIG. 1 shows a vehicle 10with an associated trajectory planning system depicted at 100 inaccordance with various embodiments. In general, the trajectory planningsystem 100 determines a trajectory plan for automated driving of thevehicle 10. The vehicle 10 generally includes a chassis 12, a body 14,front wheels 16, and rear wheels 18. The body 14 is arranged on thechassis 12 and substantially encloses components of the vehicle 10. Thebody 14 and the chassis 12 may jointly form a frame. The wheels 16 and18 are each rotationally coupled to the chassis 12 near a respectivecorner of the body 14.

In various embodiments, the vehicle 10 is an autonomous vehicle and thetrajectory planning system 100 is incorporated into the autonomousvehicle 10 (hereinafter referred to as the autonomous vehicle 10). Theautonomous vehicle 10 is, for example, a vehicle that is automaticallycontrolled to carry passengers from one location to another. Theautonomous vehicle 10 is depicted in the illustrated embodiment as apassenger car, but it should be appreciated that any other vehicleincluding motorcycles, trucks, sport utility vehicles (SUVs),recreational vehicles (RVs), marine vessels, aircraft, etc., can also beused. In an exemplary embodiment, the autonomous vehicle 10 is aso-called Level Four or Level Five automation system. A Level Foursystem indicates “high automation”, referring to the drivingmode-specific performance by an automated driving system of all aspectsof the dynamic driving task, even if a human driver does not respondappropriately to a request to intervene. A Level Five system indicates“full automation”, referring to the full-time performance by anautomated driving system of all aspects of the dynamic driving taskunder all roadway and environmental conditions that can be managed by ahuman driver.

As shown, the autonomous vehicle 10 generally includes a propulsionsystem 20, a transmission system 22, a steering system 24, a brakesystem 26, a sensor system 28, an actuator system 30, at least one datastorage device 32, and at least one controller 34. The propulsion system20 may, in various embodiments, include an internal combustion engine,an electric machine such as a traction motor, and/or a fuel cellpropulsion system. The transmission system 22 is configured to transmitpower from the propulsion system 20 to the vehicle wheels 16 and 18according to selectable speed ratios. According to various embodiments,the transmission system 22 may include a step-ratio automatictransmission, a continuously-variable transmission, or other appropriatetransmission. The brake system 26 is configured to provide brakingtorque to the vehicle wheels 16 and 18. The brake system 26 may, invarious embodiments, include friction brakes, brake by wire, aregenerative braking system such as an electric machine, and/or otherappropriate braking systems. The steering system 24 influences aposition of the of the vehicle wheels 16 and 18. While depicted asincluding a steering wheel for illustrative purposes, in someembodiments contemplated within the scope of the present disclosure, thesteering system 24 may not include a steering wheel.

The sensor system 28 includes one or more sensing devices 40 a-40 n thatsense observable conditions of the exterior environment and/or theinterior environment of the autonomous vehicle 10. The sensing devices40 a-40 n can include, but are not limited to, radars, lidars, globalpositioning systems, optical cameras, thermal cameras, ultrasonicsensors, and/or other sensors. In various embodiments, the vehicle 10includes a radar system including an array of radar sensors, the radarsensors being located at various locations along the vehicle 10. Inoperation, a radar sensor sends out an electromagnetic pulse 48 that isreflected back at the vehicle 10 by one or more objects 50 in the fieldof view of the sensor. The reflected pulse 52 appears as one or moredetections at the radar sensor.

The actuator system 30 includes one or more actuator devices 42 a-42 nthat control one or more vehicle features such as, but not limited to,the propulsion system 20, the transmission system 22, the steeringsystem 24, and the brake system 26. In various embodiments, the vehiclefeatures can further include interior and/or exterior vehicle featuressuch as, but are not limited to, doors, a trunk, and cabin features suchas ventilation, music, lighting, etc. (not numbered).

The controller 34 includes at least one processor 44 and a computerreadable storage device or media 46. The processor 44 can be any custommade or commercially available processor, a central processing unit(CPU), a graphics processing unit (GPU), an auxiliary processor amongseveral processors associated with the controller 34, a semiconductorbased microprocessor (in the form of a microchip or chip set), amacroprocessor, any combination thereof, or generally any device forexecuting instructions. The computer readable storage device or media 46may include volatile and nonvolatile storage in read-only memory (ROM),random-access memory (RAM), and keep-alive memory (KAM), for example.KAM is a persistent or non-volatile memory that may be used to storevarious operating variables while the processor 44 is powered down. Thecomputer-readable storage device or media 46 may be implemented usingany of a number of known memory devices such as PROMs (programmableread-only memory), EPROMs (electrically PROM), EEPROMs (electricallyerasable PROM), flash memory, or any other electric, magnetic, optical,or combination memory devices capable of storing data, some of whichrepresent executable instructions, used by the controller 34 incontrolling the autonomous vehicle 10.

The instructions may include one or more separate programs, each ofwhich includes an ordered listing of executable instructions forimplementing logical functions. The instructions, when executed by theprocessor 44, receive and process signals from the sensor system 28,perform logic, calculations, methods and/or algorithms for automaticallycontrolling the components of the autonomous vehicle 10, and generatecontrol signals to the actuator system 30 to automatically control thecomponents of the autonomous vehicle 10 based on the logic,calculations, methods, and/or algorithms. Although only one controller34 is shown in FIG. 1, embodiments of the autonomous vehicle 10 caninclude any number of controllers 34 that communicate over any suitablecommunication medium or a combination of communication mediums and thatcooperate to process the sensor signals, perform logic, calculations,methods, and/or algorithms, and generate control signals toautomatically control features of the autonomous vehicle 10.

The trajectory planning system 100 navigates the autonomous vehicle 10based on a determination of objects and/their locations within theenvironment of the vehicle. In various embodiments the controller 34performs calculations to record probabilities in an occupancy grid basedon detections from the radar system of the vehicle 10. The processoruses the occupancy grid in order to make decisions for navigating thevehicle 10. Upon determining various parameters of the object, such asrange, azimuth, elevation, velocity, etc., from the occupancy grid, thecontroller 34 can operate the one or more actuator devices 42 a-n, thepropulsion system 20, transmission system 22, steering system 24 and/orbrake 26 in order to navigate the vehicle 10 with respect to the object50. In various embodiments, the controller 34 navigates the vehicle 10so as to avoid contact with the object 50.

In one aspect, the processor 44 creates an occupancy grid using a dualinverse sensor model (ISM). An occupancy grid is a three-dimensionalrepresentation of the environment of the vehicle 10. The occupancy gridrepresents a volume of the environment that can be sampled using theradar system and is therefore limited in range, azimuth and elevation.The occupancy grid is described using spherical polar coordinates (ρ, θ,φ) centered at the sensor. The occupancy grid is partitioned intothree-dimensional bins characterized by (ρ, θ, φ) and stores or recordsprobabilities for radar detections in bins corresponding to the range(ρ), azimuth (θ) and elevation (φ) of the detection. When navigating avehicle, the values of the occupancy grid are accessed in order toprovide a probabilistic representation of the environment and of objectstherein. The values within the occupancy grid can thus be used to informthe processor 44 of objects, allowing the processor 44 to performoperations at the vehicle 10 in order to prevent the vehicle 10 frommaking contact with the objects.

The occupancy grid is created and updated using a dual inverse sensormodel (ISM) that includes a positive inverse sensor model and a negativeinverse sensors model. An inverse sensor model is a model that specifiesa distribution of state variables (i.e., in the occupancy grid) based onmeasurements. The positive ISM assigns a conditional occupancyprobability to a bin of the occupancy grid based on a measurementindicating the presence of a detection at a corresponding location inthe environment. The positive ISM uses probabilities to represent thepresence of the object at a given location in the environment. Thenegative ISM tracks areas in which no detections occur and assignssuitable probabilities to the corresponding bins. In one embodiment, thepositive ISM and negative ISM are updated separately using the radarobservations, where radar observation includes regions or directions inwhich detections occur and regions or directions in which no detectionsare found. The regions or directions in which no directions are found(no-detection directions) are used to update the negative ISM and theregions or direction in which directions are found (with-detectiondirections) are used to update the positive ISM. The negative ISM andpositive ISM are and then combined in order to create an updated dualISM. The updated dual ISM is used to create a static occupancy grid.

To derive an ISM, one starts with a probabilistic description of thesensor, i.e., a distribution of sensor readings given a target at acertain location X. Bayes theorem is applied in order to obtain theprobability of the target being at location X given the sensor reading.In order to create the occupancy grid, the representation of the spacesurrounding the vehicle 10 is discretized by introducing athree-dimensional grid, such as shown in FIG. 2. The grid cells of thethree-dimensional grid are considered to be independent of each other sothat their occupancy probabilities satisfy the equation:p(m ₁ ,m ₂ , . . . ,m _(N) |X)=Π_(k=1) ^(N)(m _(k) |X)  Eq. (1)where m_(k)=0 or 1. An empty k^(th) grid point has m_(k)=0 and anoccupied k^(th) grid point has m_(k)=1.

FIG. 2 shows an illustrative occupancy grid 200. A spherical polarcoordinate system 225 is centered on a sensor 202 of a radar system. Thesensor 202 is located at the origin of the spherical polar coordinatesystem 225. For illustrative purposes, a first detection 204 and asecond detection 212 are shown. For range variables, the first detection204 lies within a particular range bin. For angular variables, the firstdetection 204 lies within an azimuthal bin 206 and an elevation bin 208.The azimuthal bin 206 and elevation bin 208 define a first solid anglebin 210 covering an area on a spherical surface centered at the sensor202. The first solid angle bin 210 can be determined by projecting a rayfrom the sensor 202 through the first detection 204 onto the sphericalsurface and recording the bin through which the ray passes. Similarly,the second detection 212 lies within an azimuthal bin 214 and anelevation bin 216. The azimuthal bin 214 and elevation bin 216 define asecond solid angle bin 218 of the spherical surface. The second solidangle bin 218 can also be determined by projecting a ray from the sensor202 through the second detection 212 onto the spherical surface andrecording the bin through which the ray passes.

In various embodiments, it is useful to take a logarithm of theprobability (i.e., the “odds”) in order to work with log(probability) or“log(odds)”. An odds ratio is defined as the ratio between theprobability of a cell being occupied and the probability of the cellbeing empty, which is given by Eq. (2):

$\begin{matrix}{O_{k} = {\frac{p\left( {m_{k} = {1❘X}} \right)}{p\left( {m_{k} = {0❘X}} \right)} = \frac{p\left( {m_{k} = {1❘X}} \right)}{1 - {p\left( {m_{k} = {1❘X}} \right)}}}} & {{Eq}.\mspace{11mu}(2)}\end{matrix}$Using the logarithm of the odds Ok produces a log(odds) values L_(k):

$\begin{matrix}{L_{k} = {{\log\mspace{11mu} O_{k}} = {\log\left\lbrack \frac{p\left( {m_{k} = {1❘X}} \right)}{1 - {p\left( {m_{k} = {1❘X}} \right)}} \right\rbrack}}} & {{Eq}.\mspace{11mu}(3)}\end{matrix}$The log(odds) values simplify the process of updating the ISMs becausethey are additive in the logarithm domain. They can also be computedrecursively for any iteration n using simple addition:L _(k) ^(n) =L _(k) ^(n-1) +ΔL _(k) ^(n) −L _(k) ⁰  Eq. (4)where ΔL_(k) ^(n) is the change in the log-likelihood at cell kfollowing measurements taken at time n. ΔL_(k) ⁰ is often, but notnecessarily, taken to be zero.

The positive ISM is used to estimate ΔL_(k) ^(n) at various locationswith detection bins in the occupancy grid therefore is used to estimateoccupancy probabilities at the with-detection bins of the occupancy gridfor a selected moment in time. Due to high angular resolution, highdetection probability and low false alarm rates, positive ISM models arerepresented by delta function-like along the azimuth and elevation.

For the positive ISM, the spatial uncertainties in detections arecharacterized by variances (σ_(ρ) ², σ_(θ) ², σ_(φ) ²) in range, azimuthand elevation, respectively. These uncertainties are considered to beuncorrelated. In one embodiment, the probability density function for adetection is approximately Gaussian, as shown in Eq. (5):p(ρ,θ,φ)˜N(ρ−ρ₀,σ_(ρ) ²)N(θ−θ₀,σ_(θ) ²)N(φ−φ₀,σ_(φ) ²)  Eq. (5)

A detection i at location (ρ_(i), θ_(i), φ_(i)) with intensity I_(i)influences cells inside volume ΔΩ^((i))=[0≤ρ≤ρ_(i)+3σ_(ρ), σ_(i)±3σ_(θ),φ_(i)±3σ_(φ)]. For a cell M that is fully or partially inside ΔΩ, theconditional occupancy probability changes by:ΔP _(pos) ^((i))(M)=W(I _(i))∫_(ΔΩ) _((i)) _(∩M) p ^((i))(ρ,θ,φ)dΩ  Eq.(6)where W(I_(i)) is an empiric weight factor that considers strongerdetections to have a larger contribution to the occupancy probabilitythan weaker detections.

For ease of storage and increasing updating speed, the occupancy gridstores the log(odds) rather than odds. The log(odds) for a bin of thepositive ISM can be updated using:

$\begin{matrix}{{L_{n}(M)} = {{L_{n - 1}(M)} + {\Sigma_{i}{\log\left( \frac{\Delta\;{P_{pos}^{(i)}(M)}}{P_{FA}} \right)}}}} & {{Eq}.\mspace{11mu}(7)}\end{matrix}$

The positive ISM can be computed using brute force by calculating theintegral:ΔP _(pos) ^((i))(M)∝∫_(ΔΩ) _((i)) _(∩M) p _(pos) ^((i))(ρ,θ,φ)dΩ  Eq.(8)which can prove to be inefficient and time-consuming. However anapproximation of the interval can be calculated by separating orfactoring Eq. (8) into its angular and radial components, as shown inEq. (9):∫_(ΔΩ) _((i)) _(∩M) p ^((i))(ρ,θ,φ)dΩ=∫ _(ΔΩ) _((i)) _(∩M) p _(ang)^((i))(θ,φ)cos θdΩdφ×∫ _(ΔΩ) _((i)) _(∩M) p _(rad) ^((i))(ρ)ρ² dρ≈P_(and)(θ_(i),φ_(i) ,M)×P _(rad)(ρ_(i) ,M)  Eq. (9)The angular and radial components can be considered to be independent ofeach other. Therefore, angular probability values can be determined forthe angular component and radial probability values can be determinedfrom the radial component and these probability values can be multipliedtogether in order to determine a probability value of a bin of thepositive ISM. Factoring Eq. (9) allows for calculating P_(ang) (θ_(i),φ_(i), M) and P_(rad)(ρ_(i), M) values previously so that such valuescan be stored in a database and quickly accessed. To calculate theprobabilities, the values are drawn from the database and multipliedtogether. In the radial direction, the behavior of +ΔL_(n) ^(k) ispostulated using the probability graphs shown in FIGS. 3a and 3 b.

FIG. 3a (prior art) shows a radial probability graph 300 for creating orupdating an occupancy grid based on an object's location. Forillustrative purposes, the object is located a range or distance r fromthe sensor. The probability associated with the detection at range r isgiven by a probability 1. For the distances between the sensor and theobject, the probability value is zero, since a detection at range rindicates no objects between the sensors and the object. The remainingdistance between the object and the maximum range can be assigned aprobability value of ½, indicating that there is an even probabilitythat another object is located between the object and the maximum range,even if it is undetected.

FIG. 3b (prior art) shows a log(odds) model for a radial probabilitygraph 302 of an object located at range M₀ from the sensor. Theprobability associated with detection at M₀ is given by a positiveprobability |α| Since a detection is located at M₀, the likelihood of anobject between the sensor and M₀ is low. Otherwise, the object would bedetected at a different radial location. Thus a negative probability−|β| is assigned to the radial distances between the sensor and M₀. Theremaining distance between the location M₀ and the maximum range can beassigned a zero probability value.

FIG. 4 shows an occupancy grid 400 illustrating with-detection regionsand no-detection regions. The occupancy grid 400 shows a cross-sectionof a surface area of the occupancy grid highlighting regions of positivedetection (with-detection regions) and negative detection (no-detectionregions). Positive regions 406 and 408 are filled with probabilityvalues or log(odds) values using rules of the positive ISM details abovewith respect to FIGS. 2 and 3. Illustrative regions 410 and 412 areregions in which there are no detections. Thus, it is useful to be ableto update grid probability values to represent the lack of detectionsassociated with the appropriate azimuth and elevation. The negative ISMdiscussed herein updates the occupancy grid 400 for no-detectionregions.

The negative ISM expresses the fact that if a certain direction in spaceincludes no detections, the occupancy probability within thecorresponding solid angle bin should decrease or go down. The negativeISM induces negative changes in the occupancy likelihood in cells of theoccupancy grid for which there is a lack of detections in thecorresponding direction of arrival (no-detection direction). Therefore,a probability value in a selected bin of the occupancy grid due to thepresence of a detection in the direction corresponding to the bin duringa previous time step can updated and reduced when no detections areoccurring in the direction during more recent time steps. The log(odds)for a direction in which there is no detection can be provided by Eq.(10):

$\begin{matrix}{{\Delta\;{{LO}_{neg}(\rho)}} = {\log\left( \frac{1 - {p_{e}(\rho)}}{1 - P_{0}} \right)}} & {{Eq}.\mspace{11mu}(10)}\end{matrix}$for which:p _(e)(ρ)=β(ρ_(max)−ρ)  Eq. (11)where ρ_(max) is a maximum range of the sensor and P₀ is a modelparameter of the sensor. Since for any radar, the deduction probabilitydecreases with distance, the negative offset of Eq. (10) decreases forbins of the occupancy grid at longer ranges. In an alternativeembodiment, the negative ISM can assume a linear decay of the log-oddswith range, as shown in Eq. (12):ΔL _(neg)(ρ)=−|α|−|β|(ρ_(max)−ρ)  Eq. (12)

FIG. 5 shows an illustrative quad-tree structure 500 that can be used tostore and update probability values for a negative ISM. The quad-treestructure includes a plurality of levels, with each level includingnodes in the form of solid angle bins. At each level, the plurality ofnodes for the level cover a selected solid angle of the sensor. In oneembodiment, the selected solid angle is the field of view of a sensor. Anode or surface area at one level is related to nodes at a lower levelby a branching operation. Referring first to level 1, the area A coversa selected solid angle of the sensor. The area A can be partitioned intofour separate solid angle areas (A₁, A₂, A₃, A₄) at the second level viathe branching operation. The entirety of the solid angle areas (A₁, A₂,A₃, A₄) of the second level covers the area A at the first level. Eachof these solid angle areas (A₁, A₂, A₃, A₄) can be further partitionedvia the branching operation into four solid angles at a third level. Forillustration, solid angle A4 at the second level is partitioned intofour solid angle areas (A₄₁, A₄₂, A₄₃, A₄₄). This process continuesuntil a level is reaches at which no further partitioning of the solidangle is possible or desirable, either by a resolution limit of thesensor or a resolution default selected by a user.

FIG. 6 illustrates use of the quad-tree structure of FIG. 5 to fill anoccupancy grid 600 using a negative ISM. An illustrative solid angle 602of an angular component of an occupancy grid 600 is shown on the leftwith two detections. On the right, the solid angle 602 of the angularcomponent is shown. Bins for which the detections are present are markedfor illustrative purposes. A portion of the solid angle 602 is coveredby area A at a first level of a quad-tree structure. Using the branchingoperation, the area A is partitioned into smaller areas A₁, A₂, A₃ andA₄.

The detections area present in areas A₂ and A₃, whereas areas A₁ and A₄have not detections present. In order to create the negative ISM.Negative ISM probabilities, such as discussed in Eqs. (8)-(10) areentered into those bins (at the lowest level of the occupancy grid) thatare within areas A₁ and A₄. However, areas A₂ and A₃ are partitioned ata next level of the quad-tree structure, because detections are foundwithin these areas.

For ease of explanation, we discuss only the area A₂. Area A₂ (a secondlevel node) is partitioned into areas A₂₁, A₂₂, A₂₃ and A₂₄. Areas A₂₁,A₂₂ and A₂₄ are devoid of detections. Therefore, suitable negative ISMprobabilities can be entered into their related bins. Area A₂₃ howeverincludes a detection and is therefore partitioned into areas at the next(third) level of the quad-tree structure.

The process continues in this manner: when an area at one level of thequad-tree structure has no detections therein, the bins associated withthe area are assigned a probability value for the negative ISM; when anarea has a detection therein, the area is subdivided into smaller areasat the next level of the quad-tree structure.

The area A₂₃ is therefore partitioned into areas A₂₃₁, A₂₃₂, A₂₃₃ andA₂₃₄. For illustrative purposes, these areas are at the last level ofthe quad-tree structure. Therefore, areas A₂₃₁, A₂₃₂ and A₂₃₄ areassigned negative ISM probability values. The area A₂₃₃ can be assigneda value using a positive ISM value computed using the Eq. (9). Thisprocess can also be used to partition area A₃ with respect to the otherdetection shown in FIG. 7.

In various embodiments, the processor 44 creates the negative ISM usingthe quad-tree structure of FIGS. 5 and 6. The negative ISM values can bestored in memory in a look-up table for ease of access. The use of thequad-tree structure increases a speed and efficiency for forming thenegative ISM.

Once the negative ISM and the positive ISM have been created and/orupdated, they are combined into a dynamic occupancy grid. The dynamicoccupancy grid therefore includes bins that have an associated dynamicprobability, meaning the probability associated with the bin changeswith each new time step or each new incoming set of detections. For abin in which a detection was recorded in a first time step, but insubsequent time steps no detection was recorded, the current probabilityis altered due to the negative ISM so that the bin has an associatedprobability that reflects the fact that no detections have been recordedmore recently. In other words the probability that is assigned to thebin due to the detection in the first time step is reduced over time dueto corrections using the empty space weight.

FIG. 7 shows a positive ISM 700, a negative ISM 702, and a dual ISM 704for the occupancy grid that combines the values of positive ISM 700 andthe values of the negative ISM 702. The negative ISM 702 influences allof the bins in the no-detection directions within the field of view butdoes not affect bins in with-detection directions. On the other hand,for the positive ISM 700, the log(odds) are zero except inside a narrowangle around a detection. Inside this angle, the log(odds) are asindicated by the radial graph of FIG. 3 b.

By updating the occupancy grid using both the positive ISM 700 and thenegative ISM 702, the probability values associated with the bins of theoccupancy grid changes with each new time step or each new incoming setof detections to reflect the a current state of the environment of thevehicle.

FIG. 8 shows a flow diagram 800 illustrating a method for producing anoccupancy grid that dynamically represents the environment of thevehicle 10. A detection system, such as a radar system 802, obtains oneor more detections 806. The radar system 802 includes a sensor thatobtains detections related to objects within an environment of thevehicle during each of a plurality of time-separated frames. The radarsystem 802 obtains signals or detections 806 based on a range, azimuthand elevation of an object as well as its Doppler frequency or velocity.In the angular directions, the detections 806 are defined over a solidangle defined by the azimuth and elevation limits of the sensor. Anodometer 804 or other suitable velocity meter provides a speed of thevehicle 10 to a self-motion estimation module 808. The motion of thevehicle is provided to the radar detections in order to separate thedetections into a static set 810 of detections and a dynamic set 812 ofdetections. The static set 810 includes objects within the environmentthat do not move or are stationary within the environment, such asparked vehicles, buildings, signs, and other permanent fixtures in theenvironment. The dynamic detections 806 are related to objects that movewithin the environment, such as moving vehicles, pedestrians in motion,bicyclists, etc.

The static set 810 of detections and the dynamic set 812 of detectionsare provided to a clustering and outlier removal module 814 that filtersthe detections to remove noisy signals from the static set 810 ofdetections and dynamic set 812 of detections. In addition, thedetections are grouped into clusters depending on their relativeproximity to each other. Outlier detections are generally removed fromconsideration.

From clustering and outlier removal module 814, the filtered static set816 of detections and the filtered dynamic set 818 of detections areprovided to an empty space update module 828. The empty space updatemodule 828 creates an occupancy grid that records the locations at whichno detections are found in a selected frame. The record of empty spacecan be used along with the updated static occupancy grid 826 in order toupdate a dynamic occupancy grid 830 to changes to reflect the currentnature of objects in the environment of the vehicle in the form of adynamic occupancy grid 832.

The filtered static detections 816 are provided to an update loop 820that updates a static occupancy grid in order to reflect the changingnature of the environment. The update loop 820 includes a staticoccupancy grid history 822 that stores the previous version of thestatic occupancy grid. The static occupancy grid history 822 and thevelocity of the vehicle is used to resampling the static occupancy grid.The resampled occupancy grid 824 and the filtered static detections 816are used to produce an updated static occupancy grid 826. For asubsequent updating step, the updated static occupancy grid 826 is usedas the static occupancy grid history 822. The updated static occupancygrid 826 is provided to a dynamic occupancy update module 830 in orderto provide a dynamic occupancy grid 832.

FIGS. 9 and 10 illustrative differences in radar detections over timefor a system that does not use the negative ISM for the occupancy gridvs. an occupancy grid disclosed herein that uses the negative ISM. FIG.9 shows a display of an illustrative radar field in a scenario in whichan object is passing in front of the vehicle, wherein the radar field isformed from an occupancy grid that does not use the negative ISM. Theobject is at a first location at time to, a second location at time t₁and a third location at time t₂. However, at time t₂, the radar systemis showing a persistent streak 902 of the object extending from thelocation of the object at time to to the location of the object at timet₂. The persistent streak 902 therefore indicates an object at time t₂at locations at which the object no longer is present.

FIG. 10 shows the display of the illustrative radar field in the samescenario as FIG. 9, wherein the radar field is formed from an occupancygrid that uses the negative ISM disclosed herein. Rather than apersistent streak 902 as seen in FIG. 9, at time t₀, the radar fieldshows an object at location 1002. At a later time t₁, the objects isseen to have moved from location 1002 to new location 1004. At latertime t₂, the radar field shows the object has once again moved, thistime from location 1004 to location 1006. The radar field at each timestep therefore shows only a localized representation of the object thatis a suitable representation for the particular time step.

While the above disclosure has been described with reference toexemplary embodiments, it will be understood by those skilled in the artthat various changes may be made and equivalents may be substituted forelements thereof without departing from its scope. In addition, manymodifications may be made to adapt a particular situation or material tothe teachings of the disclosure without departing from the essentialscope thereof. Therefore, it is intended that the present disclosure notbe limited to the particular embodiments disclosed, but will include allembodiments falling within the scope thereof.

What is claimed is:
 1. A method of mapping an environment, comprising:computing a plurality of radial components and a plurality of angularcomponents for a positive inverse sensor model (ISM) of an occupancygrid; obtaining a detection at a sensor from an object in an environmentsurrounding a vehicle; selecting a radial component corresponding to arange of the detection from the plurality of radial components andselecting an angular component corresponding to an angle of thedetection from the plurality of angular components; multiplying theselected radial component and the selected angular component to createan occupancy grid for the detection; and mapping the environment usingthe occupancy grid.
 2. The method of claim 1, wherein the ISM furthercomprises a negative ISM and a probability value of the negative ISM isassigned using a quad-tree structure of the occupancy grid.
 3. Themethod of claim 2, wherein a node of the quad-tree structure correspondsto a solid angle and a first level of the quad-tree structure includessolid angle bins that combine to cover a field of view of the sensor. 4.The method of claim 3, further comprising partitioning a solid angle binat a level of the quad-tree structure into a plurality of sub solidangles at a sub level of the quad-tree structure when the solid anglebin at the level is includes the detection.
 5. The method of claim 4,further comprising assigning a probability value to a solid angle binfor which there is no detection, wherein the probability value reflectsan absence of the detection in the solid angle bin.
 6. The method ofclaim 2, further comprising combining the probability values from thenegative ISM with a probability value from the positive ISM to createthe occupancy grid.
 7. The method of claim 1, further comprisingnavigating the vehicle with respect to the object based on the mappingof the environment.
 8. A system for mapping an environment at a vehicle,comprising: a sensor configured to obtain a detection from an object inan environment surrounding the vehicle; and a processor configured to:compute a plurality of radial components and a plurality of angularcomponents for a positive inverse sensor model (ISM) of an occupancygrid; select a radial component corresponding to a range of thedetection from the plurality of radial components and selecting anangular component corresponding to an angle of the detection from theplurality of angular components; multiply the selected radial componentand the selected angular component to create an occupancy grid for thedetection; and map the environment using the occupancy grid.
 9. Thesystem of claim 8, wherein the processor is further configured to assigna probability value of a negative ISM of the occupancy grid using aquad-tree structure of the occupancy grid.
 10. The system of claim 9,wherein a node of the quad-tree structure corresponds to a solid angleand a first level of the quad-tree structure includes solid angle binsthat combine to cover a field of view of the sensor.
 11. The system ofclaim 10, wherein the processor is further configured to partition asolid angle bin at a level of the quad-tree structure into a pluralityof sub solid angles at a sub level of the quad-tree structure when thesolid angle bin at the level includes the detection.
 12. The system ofclaim 11, wherein the processor is further configured to assign aprobability value to a solid angle bin for which there is no detection,wherein the probability value reflects an absence of the detection atthe solid angle bin.
 13. The system of claim 9, wherein the processor isfurther configured to combine the probability values from the negativeISM with a probability value from a positive ISM to create the occupancygrid.
 14. The system of claim 8, wherein the processor is furtherconfigured to navigate the vehicle with respect to the object based onthe mapping of the environment.
 15. A vehicle, comprising: a sensorconfigured to obtain a detection from an object in an environmentsurrounding the vehicle; and a processor configured to: compute aplurality of radial components and a plurality of angular components fora positive inverse sensor model (ISM) of an occupancy grid; select aradial component corresponding to a range of the detection from theplurality of radial components and selecting an angular componentcorresponding to an angle of the detection from the plurality of angularcomponents; multiply the selected radial component and the selectedangular component to create an occupancy grid for the detection; and mapthe environment using the occupancy grid.
 16. The vehicle of claim 15,wherein the processor is further configured to assign a probabilityvalue to a negative ISM of the occupancy grid using a quad-treestructure of the occupancy grid.
 17. The vehicle of claim 16, wherein anode of the quad-tree structure corresponds to a solid angle and a firstlevel of the quad-tree structure includes solid angle bins that combineto cover a field of view of the sensor.
 18. The vehicle of claim 17,wherein the processor is further configured to partition a solid anglebin at a level of the quad-tree structure into a plurality of sub solidangles at a sub level of the quad-tree structure when the solid anglebin at the level includes the detection.
 19. The vehicle of claim 18,wherein the processor is further configured to assign a probabilityvalue to a solid angle bin for which there is no detection, wherein theprobability value reflects an absence of the detection at the solidangle bin.
 20. The vehicle of claim 16, wherein the processor is furtherconfigured to combine the probability values from the negative ISM witha probability value from a positive ISM to create the occupancy grid.